Momentum of a proton in de Broglie wavelength

In summary, the de Broglie wavelength of protons accelerated from rest through a potential V can be calculated using the equation λ=h/p, where h is Planck's constant. Using the conservation of energy and the equation p=mv, it can be determined that the wavelength is h/\sqrt{}2meV, as shown in answer B.
  • #1
Alb
3
0

Homework Statement



In quantum mechanics the de Broglie wavelength of an object depends
on its momentum according to λ=h/p where h is Planck's constant.
Protons of charge e and mass m are accelerated from rest through a
potential V. What is their de Broglie wavelength?

A) [itex]2h/\sqrt{}meV[/itex]
B) [itex]h/\sqrt{}2meV[/itex]
C) h[itex]\sqrt{}meV[/itex]
D) [itex]h/eV[/itex]

Homework Equations



I don't know.

The Attempt at a Solution



I just don't know what I have to search for to solve it.
How can I express p with e and V?
 
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  • #2
Hello there.
As you probably know p=mv. From conservation of energy u have mv^2/2 = eU, here you can solve for the velocity v. After that you can use it to end up with answer B)
 
  • #3
Thanks.
 

What is the momentum of a proton in de Broglie wavelength?

The momentum of a proton in de Broglie wavelength is calculated using the formula p = h/λ, where p is the momentum, h is Planck's constant, and λ is the de Broglie wavelength. This formula is derived from the de Broglie equation, which states that every particle has a wave-like nature with a wavelength inversely proportional to its momentum.

How is the de Broglie wavelength of a proton determined?

The de Broglie wavelength of a proton can be determined by dividing Planck's constant by the momentum of the proton. This can be calculated using the mass and velocity of the proton using the formula p = mv, where m is the mass and v is the velocity. The resulting wavelength is the de Broglie wavelength of the proton.

What is the significance of the de Broglie wavelength of a proton?

The de Broglie wavelength of a proton is significant because it demonstrates the wave-particle duality of matter. It shows that particles, such as protons, can exhibit wave-like behavior and have a wavelength associated with them. This concept was a major development in quantum mechanics and has helped scientists better understand the behavior of particles at the subatomic level.

Can the de Broglie wavelength of a proton be measured?

Yes, the de Broglie wavelength of a proton can be measured using various experimental techniques. One common method is using a diffraction grating, which causes the proton to diffract and creates an interference pattern that can be used to determine its wavelength. Other methods, such as electron microscopy, can also be used to measure the de Broglie wavelength of a proton.

How does the momentum of a proton change with its de Broglie wavelength?

The momentum of a proton is inversely proportional to its de Broglie wavelength. This means that as the wavelength increases, the momentum decreases and vice versa. This relationship is a fundamental principle in quantum mechanics and plays a crucial role in understanding the behavior of particles at the atomic and subatomic level.

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